help diagnosing an Apple IIe, please.

[adric22 <adric22@yahoo.com>]

Okay, so I just got this Apple IIe and color monitor today.  I'm an
old-school Commodore geek, and I'm very technically oriented.  I just
don't know much about the Apple II series.

The computer appears to have two problems.  First problem seems to be
with the power supply.  If I turn the machine on, it will power on one
time.  I can use it a bit, and turn it off.  Once I do that, it will
not turn on again.  Instead the LED lights up part of the way.  I can
unplug it from the wall for a minute or so and plug it back in and it
will turn on again.

The second problem is with the display.  The characters are a little
corrupted looking.  You can read what it says, but the characters are
missing parts and some pixels of the characters seem to flicker on and
off.  Although a few times I've managed to turn it on and everything
looks fine.  Perhaps it is related to the power supply issue?  Or is
it a bad character rom, or video chip?